Extract

The actual effects of selection and assortative mating on the variability and correlation of organs have long been known. The general numerical resemblance between the correlations found for gametic characters on the Mendelian hypothesis for random sampling and mating and those computed from actual data is now also well established, though the fundamental difficulties in the way of reconciling the deductions tyom that hypothesis with the distributions and regressions actually obtained for, say, coat-colour in mice, have not been diminished. It is of importance, therefore, to ascertain what conclusions can be reached as regards the numerical effects of selection and of assortative mating on the basis of the Mendelian mechanism, and to this end an analytical investigation was entered Upon on a more general and rigorous foundation than any which have previously been used to attempt to solve the problem. Dealing first with the correlations for gametic characters. In general terms, it was established that the effect of taking a selected sample instead of a random one from a population showing a zero coefficient of assortative mating would be to find the ancestral and fraternal correlations within that sample less than those of a random sample, so long as the variability was diminished by the selection. If an ancestor be selected, the correlations between that ancestor and descendants diminish in geometrical progression. On the whole, selection of parents appears to affect the correlations between them and their offspring to a greater extent than it affects the relationship between those offspring themselves. For all ancestral cases the regressions appear to be more stable properties of a particular population than the corresponding correlations; frequently the regression of offspring on ancestor is the same as for a random sample, though the correlation is changed. The investigation also brought out that the value 0.5 in each case for the fraternal and parental correlations obtained when random samples of a general Mendelian population are dealt with does not depend upon the fact that the samples are random ones, but upon the fact that for such a population the frequency of the heterozygote is twice the geometric mean of the frequencies of the dominant and recedent homozygotes.

Footnotes

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